Exterior algebra resolutions arising from homogeneous bundles

Abstract

We describe resolutions of general maps (resp. general symmetric and skew-symmetric maps) $E^a \rightarrow E(1)^b$ given by linear forms over the exterior algebra $E$. Via the BGG-correspondence we describe the associated coherent sheaves. We also show how representation theory of algebraic groups enables one to solve these types of problems for much larger classes of maps.